**A q-analog of Ljunggren's binomial congruence**

Armin Straub — Discrete Mathematics and Theoretical Computer Science — Special volume for FPSAC 2011 — 2011, Pages 897-902

## Abstract

We prove a \(q\)-analog of a classical binomial congruence due to Ljunggren which states that \[ \binom{a p}{b p} \equiv \binom{a}{b} \] modulo \(p^3\) for primes \(p\ge5\). This congruence subsumes and builds on earlier congruences by Babbage, Wolstenholme and Glaisher for which we recall existing \(q\)-analogs. Our congruence generalizes an earlier result of Clark.http://dmtcs.episciences.org/2962

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## BibTeX

@article{qljunggren-2011, author = {Armin Straub}, title = {A $q$-analog of {L}junggren's binomial congruence}, journal = {Discrete Mathematics and Theoretical Computer Science}, year = {2011}, pages = {897--902}, }